Geometric properties of the chaotic saddle responsible for supertransients in spatiotemporal chaotic systems

Abstract

Superlong chaotic transients have been observed commonly in spatiotemporal chaotic dynamical systems. The phenomenology is that trajectories starting from random initial conditions behave chaotically for an extremely long time before settling into a final nonchaotic attractor. We demonstrate that supertransients are due to nonattracting chaotic saddles whose stable manifold measures have fractal dimensions that are arbitrarily close to the phase-space dimension. Numerical examples using coupled map lattices are given.

title = "Geometric properties of the chaotic saddle responsible for supertransients in spatiotemporal chaotic systems",

abstract = "Superlong chaotic transients have been observed commonly in spatiotemporal chaotic dynamical systems. The phenomenology is that trajectories starting from random initial conditions behave chaotically for an extremely long time before settling into a final nonchaotic attractor. We demonstrate that supertransients are due to nonattracting chaotic saddles whose stable manifold measures have fractal dimensions that are arbitrarily close to the phase-space dimension. Numerical examples using coupled map lattices are given.",

N2 - Superlong chaotic transients have been observed commonly in spatiotemporal chaotic dynamical systems. The phenomenology is that trajectories starting from random initial conditions behave chaotically for an extremely long time before settling into a final nonchaotic attractor. We demonstrate that supertransients are due to nonattracting chaotic saddles whose stable manifold measures have fractal dimensions that are arbitrarily close to the phase-space dimension. Numerical examples using coupled map lattices are given.

AB - Superlong chaotic transients have been observed commonly in spatiotemporal chaotic dynamical systems. The phenomenology is that trajectories starting from random initial conditions behave chaotically for an extremely long time before settling into a final nonchaotic attractor. We demonstrate that supertransients are due to nonattracting chaotic saddles whose stable manifold measures have fractal dimensions that are arbitrarily close to the phase-space dimension. Numerical examples using coupled map lattices are given.